Christopher is 2 times as old as Vanessa. 28 years ago, Christopher was 9 times as old as Vanessa. How old is Vanessa now?
Explanation: We can use the given information to write down two equations that describe the ages of Christopher and Vanessa. Let Christopher's current age be $c$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $c = 2v$ 28 years ago, Christopher was $c - 28$ years old, and Vanessa was $v - 28$ years old. The information in the second sentence can be expressed in the following equation: $c - 28 = 9(v - 28)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = 2v$ . Substituting this into our second equation, we get: $2v$ $-$ $28 = 9(v - 28)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $2 v - 28 = 9 v - 252$ Solving for $v$ , we get: $7 v = 224.$ $v = 32$.